Centrality measures have been thoroughly studied for single-layer networks. These measures
include Katz centrality, subgraph centrality, and total communicability with respect to a
node; see, e.g., [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. In this section, we introduce analogues
of these measures for multilayer networks using the adjacency tensor and the Einstein
product. We limit our discussion in this and the following sections to unweighted
multilayer networks with only one kind of connections in each layer. Thus, the adjacency
tensor is a square 4th-order tensor. The extension to general weighted multilayer
networks, i.e., to multilayer networks with more than one kind of connections in each
layer, and with positive node-weights, is straightforward.
